Adaptive Local Loop Shaping and Inverse-based Youla-Kucera Parameterization with Application to Precision Control
In this dissertation we discuss loop-shaping algorithms that bring enhanced servo performance at multiple local frequency regions. These local loop shaping (LLS) algorithms are motivated by several new demands in practical control systems such as hard disk drives in information storage industry, wafer scanners in semiconductor manufacturing, active steering in automotive vehicles, and active suspension in structural vibration rejection. We will examine how knowledge about the disturbance/reference characteristics can be utilized, both offline and online, to customize the servo system for meeting the control challenges.
Along the way, we investigate several design concepts and methodologies. First, in Youla-Kucera (YK) parameterization--the parameterization of all stabilizing linear controllers--we develop plant factorizations based on selective model inversion, which safely inverts a (possibly nonminimum-phase) plant dynamics, using H infinity minimization and pole/zero modulation. This allows us to obtain a simplified YK algorithm with strong design and tuning intuitions in practical servo. Also, with selective model inversion, it becomes quite approachable to control the waterbed effect, the result of Bode's Integral Formula in fundamental limitations of linear control design. This is achieved by utilizing add-on pole/zero placement and convex-optimization approaches to minimize the disturbance amplification in the sensitivity function, which enables the obtaining of several algorithms for enhanced repetitive control and vibration rejection.
In the third part of the dissertation, we investigate adaptive formulations to achieve online identification of the disturbance characteristics. We study the application of infinite-impulse-response (IIR) filters in YK parameterization, which brings benefits such as minimum-parameter adaptation and better convergence under noisy adaptation environments. We also provide an optimization-based approach to address the problem of robust strict positive real transfer functions, an essential requirement in adaptive control and system identification.
The discussed algorithms are then extended from the control of SISO to MISO (multi-input-single-output) plants, where we formulate a decoupled disturbance observer for estimating the equivalent input disturbance for different actuators in a MISO system.
Simulation and experimental results are obtained on the four classes of systems discussed at the beginning of this abstract. Parts of the results are performed on benchmark problems, and compared with the algorithms of peer researchers under extensive test conditions.